Dr H.G.E. (Hil) Meijer | On activation functions and spatio-temporal patterns in neural fields

Travelling waves are often observed in recordings of neural activity. They are thought to play a role in diseases such as epilepsy as well as normal function such as working memory and movement. Such waves can be studied using neural fields describing spatio-temporal neuronal activity at a macroscopic level. An important feature of a neural field model is the activation function that translates activity into input to other tissue. From an analysis point of view, it is convenient to choose a Heaviside step-function as it allows to obtain existence and stability results relatively straightforward. For modelling applications, however, the modelling choice for the Heaviside is far from realistic. Instead a sigmoidal function accounts much more for the heterogeneity of cells.

In this talk I will briefly review the analysis of waves and bumps based on the Heaviside activation function. I will then discuss a framework for numerical continuation to study waves and bumps. We then consider how bifurcation diagrams (stability and existence) change as the slope of a sigmoidal activation function is varied. I end by a second modification of the activation function modelling depolarization block motivated by recordings of epileptic activity. This results in a travelling front with inhibitory activity leading instead of the typical excitation.

Poster